How long will it take to plate out each of the following with a current of 100.0 A? a. 1.0 kg Al

How long will it take to plate out each of the following...

Key Concepts

Faraday’s Laws of Electrolysis

Faraday’s laws state that the mass of a substance deposited or dissolved at an electrode during electrolysis is directly proportional to the total electric charge passed through the electrolyte. This principle links the macroscopic quantity of material change to the microscopic movement of electrons and is foundational for calculating how much material is deposited given a certain current and time.

Stoichiometry of Electrochemical Reactions

In electroplating, each ion reduction reaction requires a specific number of electrons to convert an ion into its elemental form. Understanding the stoichiometry of these electron transfer reactions is essential, as it determines the number of electrons needed per mole of metal deposited, directly affecting the calculation of total charge and deposition time.

Current and Charge Relationship

The relationship between current, time, and electric charge is described by the equation Q = I × t, where Q is the total charge, I is the current, and t is the time. This concept is critical in electrolysis calculations because it allows one to compute the duration of plating once the needed charge for deposition is known.

Conversion between Mass, Moles, and Charge

Calculations often require converting the given mass of metal to moles (using molar mass) and then relating this to the number of electrons required (via stoichiometry). This conversion is vital in determining the total charge needed to deposit a specified mass of metal, bridging the gap between the physical amount of substance and electric charge.

Transcript

00:01 In each part of this problem, we need to use concepts of electrolysis in order to calculate how long it will take to plate out, meaning to convert each one of these metals from their aqueous ion forms into their solid forms, if we run a current of 100 amps through the solution.

00:19 So starting in part a, we want to determine the time that it takes to plate out 1 .0 kilograms of aluminum from aqueous al3 plus.

00:29 So that means that the reaction that is occurring is al3 plus being reduced by adding three electrons to played out solid aluminum.

00:44 Again, we want to know how long it takes to played out 1 .0 kilograms of aluminum.

00:52 So that's our reference.

00:54 We know that we need to first convert into moles of aluminum.

00:58 So we know that one kilogram of aluminum is equal to 1 ,000 grams of aluminum.

01:08 And then from the molar mass on the periodic table, we can say that there are 26 .98 grams of aluminum for every mole of aluminum.

01:23 And then we can see from this reduction that for every one mole of aluminum, that we are plating out, that corresponds to three moles of electrons that were required to reduce al3 plus to al.

01:46 And now we multiply that by faraday's constant, which is 96 ,485 coolums per mole of electrons.

01:59 And then we have a 100 -amp current running through that al -3 -plus.

02:05 Solution so that's 100 coolums per second and we can convert the final answer from seconds into hours using the conversion of one hour is 3 ,600 seconds.

02:23 Now if we multiply all of those ratios together we should get the final answer for how long it takes to play out 1 .0 kilograms of aluminum from aqueous al3 plus and that is about 30 hours.

02:43 Now in part b we want to know how long it takes to played out 1 .0 grams of nickel solid from aqueous ni2 plus...

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